Controlling resonant photoelastic modulators

ABSTRACT

A system and method for exploiting the dependance of a photoelastic modulator&#39;s (PEM&#39;s) resonance frequency on temperature (attributable to driving amplitude and to ambient temperature) to generally improve the performance of PEMs. In one embodiment there is provided a method and system for efficiently driving a series of multiple PEMs. To this end, each of the PEMs in a stack are separately tuned, as by controlling the power dissipated in each PEM, so that the resonance frequencies of all of the PEMs converge to a common frequency. Thus, all of the PEMs are simultaneously at resonance to ensure maximum efficiency and to maintain a selected total retardation amplitude. In another embodiment of the present invention, a single-element PEM is controlled in a manner to account for the subtle changes in the PEM&#39;s resonance frequency. To this end a control method and system is provided to keep constant both the retardation amplitude of the PEM and the actual operating frequency of the PEM, which frequency need not necessarily be the resonant frequency.

This application is a national stage of PCT/US99/05586, filed Mar. 16,1999, which claims the benefit under 35 USC 119(c) of US ProvisionalApplication 60/078,069, filed Mar. 16, 1998.

TECHNICAL FIELD

This application relates to a system and method for precise control ofresonant photoelastic modulators.

BACKGROUND

A resonant photoelastic modulator (PEM) is an instrument that is usedfor modulating the polarization of a beam of light. A PEM employs thephotoelastic effect as a principle of operation. The term “photoelasticeffect” means that an optical element that is mechanically strained(deformed) exhibits birefringence that is proportional to the amount ofstrain induced into the element. Birefringence means that the refractiveindex of the element is different for different components of polarizedlight.

A PEM includes an optical element, such as fused silica, that hasattached to it a piezoelectric transducer for vibrating the opticalelement at a fixed frequency, within, for example, the low-frequency,ultrasound range of about 20 kHz to 100 kHz. The mass of the element iscompressed and extended as a result of the vibration.

The compression and extension of the optical element imparts oscillatingbirefringence characteristics to the optical element. The frequency ofthis oscillating birefringence is the resonant frequency of the opticalelement and is dependent on the size of the optical element, and on thevelocity of the transducer-generated longitudinal vibration or acousticwave through the optical element.

Retardation or retardance represents the integrated effect ofbirefringence acting along the path of electromagnetic radiation (alight beam) traversing the vibrating optical element. If the incidentlight beam is linearly polarized, two orthogonal components of thepolarized light will exit the optical element with a phase difference,called the retardance. For a PEM, the retardation is a sinusoidalfunction of time. The amplitude of this phase difference is usuallycharacterized as the retardance amplitude or retardation amplitude ofthe PEM.

In conventional PEMs, the value of the retardation amplitude isselectable by the user. Because resonant PEMs are typically driven attheir resonant frequency, stress oscillations, which are induced by thetransducer, can exhibit relatively large amplitudes. However, drivingPEMs at their resonant frequency prevents the user from controlling theoscillation frequency.

Both the size and acoustic wave velocity of a PEM depend on the opticalelement's temperature. Consequently, the resonant frequency of a PEMwill also depend on the device's temperature. In general, thistemperature depends on two factors: (1) the ambient temperature, and (2)the amplitude of the stress oscillations in the optical element. At highstress amplitudes, the amount of acoustic (mechanical) energy absorbedin the optical element can become significant. As the absorbed acousticenergy is converted to heat within the mass of the element, significanttemperature increases and corresponding shifts in the PEM's resonantfrequency can occur.

PEMs having high retardance amplitudes are required, for example, inFourier Transform spectral analysis (see, for instance, U.S. Pat. Nos.4,905,169 and 5,208,651). In such applications, spectral resolution isproportional to the PEM's retardation amplitude, and useful spectralresolutions are achieved at high amplitudes, which cannot be reached bya conventional (single) PEM.

The most direct way of achieving these high-retardation amplitudes is tostack together several PEMs. In such an arrangement it is important thatthe sum or total of the retardation amplitudes of all of the PEMsmatches the sum of the maximum retardation amplitudes of each of thePEMs in the stack.

Even if all the PEMs in a stack are driven at the same frequency, thetotal retardation amplitude of the stack may be less than the sum of themaximum retardation amplitudes of each of the PEMs in the stack. This isbecause even a relatively small spread in the resonant frequencies ofthe individual PEMs, which is fully consistent with manufacturingspecifications, results in most of the PEMs not being driven exactly atresonance. As a result, the phases of the oscillations of the individualPEMs are not the same, even though the PEMs are driven at the samefrequency, and, therefore, the total retardation amplitude is less thanthe sum of the individual amplitudes.

Furthermore, uneven heating of the individual PEMs when driven at highamplitudes may result in the individual resonant frequencies drifting byunequal amounts. Consequently, the phases of the individual PEMoscillations may further diverge as the driving amplitude is increasedor as the system warms up. This may lead to a further decrease in theefficiency of the PEM stack.

The problem of drifting operating frequencies is not limited to stackedPEM arrangements. In a conventional single PEM system, even though theretardation amplitude can be adjusted at will (within the limits set bythe maximum driving voltage provided by the electronic circuits), thesystem's operating frequency is determined by the PEM's resonantfrequency and, as explained above, thus depends on both ambienttemperature and the amplitude at which the PEM is driven. This resultsin an operating frequency that drifts with ambient temperature, as wellas during warm-up and after changes in the set retardation amplitude.Such a situation may be undesirable in certain applications where thePEM's operating frequency, as well as its amplitude, must be keptconstant.

SUMMARY OF THE INVENTION

The present invention is directed to a practical system and method forexploiting the dependence of a PEM's resonance frequency on temperature(attributable to driving amplitude and to ambient temperature) togenerally improve the performance of PEMs.

In one embodiment of the present invention, there is provided a methodand system for efficiently driving a series of multiple PEMs (such asthe stacked arrangement noted above). To this end, each of the PEMs inthe stack are separately tuned, as by controlling the power dissipatedin each PEM, so that the resonant frequencies of all of the PEMsconverge to a common frequency. Thus, all of the PEMs are simultaneouslyat resonance to ensure maximum efficiency and to maintain a selectedtotal retardation amplitude. Thus controlled, thecommon-resonance-frequency PEMs operate like a single PEM, but at a muchhigher retardation amplitude than that available from conventionalsingle-element PEMs. This result makes the multiple PEM arrangementamenable to applications, such as the above-mentioned Fourier Transformspectral analysis, that require large retardation amplitudes.

In another embodiment of the present invention, a single-element PEM iscontrolled in a manner to account for the subtle changes in the PEM'sresonant frequency. To this end, a control method and system is providedto keep constant both the retardation amplitude of the PEM and theactual operating frequency of the PEM, which frequency need notnecessarily be the resonant frequency.

Other advantages and features of the present invention will become clearupon study of the following portion of this specification and drawings.

BRIEF DESCRIPTION OF DRAWINGS

FIG. 1 is a diagram of an exemplary system for controlling multiple PEMsin accordance with one aspect of the present invention.

FIG. 2 is a block diagram of a global controller and one of the localcontrollers employed with a preferred embodiment of the presentinvention.

FIG. 3 is a diagram of a preferred embodiment of a low-pass filteremployed as an operator in the global controller.

FIG. 4 is a diagram of a preferred embodiment of a low-pass filteremployed as an operator in the local controllers.

FIG. 5 is a diagram of one preferred embodiment of a circuit forgenerating a drive voltage waveform for a PEM.

FIG. 6 is a diagram of a system for controlling a single PEM inaccordance with another aspect of the present invention.

FIG. 7 is a diagram of a system for controlling a single PEM inaccordance with another aspect of the present invention.

BEST MODES FOR CARRYING OUT THE INVENTION

The diagram of FIG. 1 depicts an exemplary system for controllingmultiple photoelastic modulators (PEMs) in accordance with one aspect ofthe present invention. In this embodiment, a series of three PEMs 20 aredepicted. The PEMs are aligned so that light from a source 22 travels ina beam 24 through each of the PEMs 20 to reach a detector 26. Theoptical aspects of the setup shown in FIG. 1 have been greatlysimplified (polarizers, etc. being omitted) for the purposes of thisdescription. Such a setup may be used, for example, in the FourierTransform spectral analysis mentioned above.

The polarization of the light 24 is modulated by the PEMs to impart aretardation amplitude in the beam that reaches the detector. In thisregard, the optical element 28 of each PEM is vibrated by an attachedpiezoelectric transducer 30, thereby to introduce into the opticalelement (such as fused silica) the oscillating birefringence discussedabove (as well as the attendant contribution to the total retardation inthe light that reaches the detector).

In accord with one embodiment of the present invention there is provideda system for controlling the multiple PEM arrangement just described sothat all of the PEMs operate at a resonant frequency and provide a totalretardation amplitude (i.e., the sum of the individual values of theretardation provided by each PEM) that precisely matches a desiredreference amplitude.

The preferred system is primarily embodied as local controllers 32, oneof which is associated with each PEM 20, and a global (system)controller 34. As will be explained, a computer 36 is, optionally,provided to facilitate operation of the global and local controllers,which computer 36 may also receive the total retardation informationcollected by the detector 26.

Before discussing the particulars of the global and local controllers,it is worth pointing out that for a single PEM to be driven at resonanceand with a selected retardation amplitude, one must, in general, controltwo parameters: (1) driving voltage and (2) driving frequency. There arealso two independent error signals that can be used by a feedback loopin order to adjust these control parameters. These are (1) theretardation amplitude error and (2) the phase error between PEM drivingvoltage and current.

The phase error relates the driving frequency to the resonant frequencyof the PEM. In the simplest situation, the phase error is zero when thetwo frequencies are equal; that is, when the PEM is driven at resonance.(In the general case, the current-voltage phase difference correspondingto resonance driving will have a non-zero, but fixed, value. In such acase, the phase error will be the difference between the current-voltagephase difference and that fixed value.)

The retardation amplitude error is the difference between actual andselected retardation amplitudes, and vanishes when the two amplitudesare equal. The retardation amplitude error can be optically determined,or approximated by the driving current amplitude error. In the followingportion of this description, the latter approximation is employed,although the former is certainly usable.

A stable feedback loop can be implemented so that the two controlparameters (driving voltage and driving frequency) always change in sucha way as to cancel the two error signals. When the two error signalshave vanished, the PEM operates at resonance and provides the selectedretardation amplitude.

FIG. 1 depicts the use of multiple (stacked) PEMs. Three PEMs are shown,although the following description will apply to groups of two or morePEMs. Thus, one can consider the series of PEMs as comprising any of anumber “n” PEMs, which number is selected to suit the retardationamplitude needs of a particular application.

When “n” PEMs are stacked, there are n+1 control parameters (the drivingvoltage amplitude for each of the “n” PEMs and the common drivingfrequency). It would appear that 2n independent error signals must becancelled (the amplitude and phase errors for each of the “n” PEMs).This would require 2n control parameters, such as “n” individual drivingvoltage amplitudes and “n” individual driving frequencies. However, inaccordance with the present invention, the control system requires onlyn+1 control parameters in the system. As a result, the PEM stack iscontrolled (i.e., all PEMs reaching a common resonant frequency whilemaintaining a selected total retardation amplitude) with only n+1control parameters.

With reference to FIG. 2, each local controller 32 (only one of which isdepicted in FIG. 2) monitors its PEM's current-voltage phase difference,as well as reference signals generated by the global controller 34,which reference signals are described more fully below. Using thesesignals, the local controller adjusts the voltage amplitude andfrequency of the PEM's driving signal.

Furthermore, each local controller 32 generates a current-voltage phaseerror signal that is provided to the global controller 34. The localcontroller also sends a local current amplitude signal to the globalcontroller 34. Also, each local controller 32 locks the phase of its PEMcurrent to a common phase reference, preferably the phase of the commonfrequency signal generated by the global controller 34, as will bedescribed.

With continued reference to FIG. 2, the exemplary one of “n” localcontrollers 32 drives its PEM by applying the following feedbackequation 1:V′=−D _(τ) ⁻¹(βεφ−γω′)the derivation of which is provided in U.S. Provisional Application No.60/078,069, hereby incorporated by reference, and from which the presentapplication claims the benefit of its filing date under 35 USC § 119e.

In the foregoing equation 1:

-   V′=the driving voltage amplitude to be applied by the local    controller to its associated PEM; V′ in equation 1 representing a    time derivative of V;-   D_(τ) ⁻¹=is an inverse integral operator (explained more below) for    a PEM having a thermal time constant τ that is the quotient of the    PEM's heat capacity and rate of heat exchange with ambient;-   β=the temperature coefficient of the PEM at resonant frequency;-   εφ=the phase difference between the PEM current and the drive signal    voltage applied to the PEM;-   γ=a coefficient determined by the individual physical    characteristics of the PEM; and-   ω′=a value corresponding to the difference between a selected    retardation amplitude (here approximated by a current amplitude) and    the “average” retardation amplitude actually applied by the PEMs and    to the sum of the phase error signals of all PEMs; this signal is    the time derivative of the common driving frequency, and is supplied    by the global controller.

With reference to FIG. 2, the local controller 32 employs avoltage-controlled oscillator (VCO) 40 receiving on line 42 a frequencyinput signal that, as described more below, sets the frequency of theconstant amplitude signal that emanates from the VCO. That signal isapplied to a multiplier 110 (shown as “X” in the figure and controlledas described below). The multiplier multiplies the amplitude of the VCOoutput signal. Thus, on line 46 there appears the drive voltage signalthat is applied to drive the transducer of the PEM 20. In short, the VCOand multiplier elements can be considered as the PEM's drive waveformgenerator.

As noted above, the present system employs as one of two error signalsthe phase errors between each of the PEM drive voltage signals and thecurrent applied to the PEM. To this end, each local controller 32 isprovided with a phase comparator 50 that receives as input the drivevoltage signal (via line 52) and a signal (line 54) that is proportionalto the current applied to the PEM. This current signal is developed by acurrent pickup “I” shown at 56.

The output of the comparator 50 (line 60) comprises the phase errorsignal εΦ for that particular PEM. As noted above, if that error isdifferent from zero (or, in general, from a predetermined nonzerovalue), then the PEM is not at resonance. As shown in FIG. 2, and withreference to equation 1, the error signal εΦ is multiplied by thetemperature coefficient β (as by a multiplier 62), inverted by inverter64 and directed to a summing circuit 66 as one of the input signals ofthat summing circuit. Also, the same signal εΦ is applied, via line 63,to the global controller 34 (as are the comparable signals from theother PEMs) for processing as described below.

The summing circuit 66 receives as its other input the signal ω′. Thissignal, which before reaching the summing circuit is multiplied by the γcoefficient at 68, is essentially representative of (1) the differencebetween the sum of all of the current amplitudes for the “n” PEMs andthe current amplitude selected by the user to be reached by the overallsystem of “n” PEMs (keeping in mind that the present analysis uses thecurrent amplitude as an approximation for the retardation amplitude) and(2) a measure of the combined phase errors εΦ_(i) from all of the PEMs.The value of ω′ is processed by the global controller (as describedbelow) in accordance with the following feedback equation 2:ω′=−μD _(τ) εI+νεΦthe derivation of which is provided in U.S. Provisional Application No.60/078,069, and where:

-   μ=a coefficient determined by the physical characteristics of the    PEMs in the system;-   D_(τ)=an integral operator, which functions as a low-pass filter;-   ωI=the signal representing the current error; the difference between    the sum of all of the current amplitudes for the “n” PEMs and the    current amplitude selected by the user to be reached by the overall    system of “n” PEMs; and-   ν=a coefficient determined by the physical characteristics of the    PEMs in the system.

Before turning to a discussion of how the reference signals (ω′ and acommon driving frequency ω) are applied at the local controllers 32,this description will next discuss how those signals are generated bythe global controller 34.

As to the current error ωI, each local controller 32 provides to theglobal controller 34 a signal indicative of the current amplitude thatis applied to that particular PEM. This is done by directing the outputof the above described current pickup 56 to a root-mean-square (rms)converter 70. This converter generates a voltage signal proportional tothe square root of the mean signal value of the PEM current. Thisvoltage signal, therefore, is a good measure of the PEM's currentamplitude “I” and is provided on line 72 to the global controller (asare the comparable signals from the other PEMs over comparable lines).

The current amplitude signals I_(I) from all of the PEMs are provided toa summing circuit 74 in the global controller, the output of which isinverted by an inverting amplifier 76 and applied to another summingcircuit 78. That circuit has as its other input a reference signalI_(ref) that represents the current amplitude selected by the user to bereached by the overall system of “n” PEMs (hence the total retardationamplitude). The output signal −ωI from this summing circuit 78represents the difference between the system current amplitude I_(ref)selected by the user and the sum of all the current amplitudes for the“n” PEMs.

The signal representing ωI passes to an operator D, which can beembodied as a low-pass filter 80 (FIG. 3) for which the followingrelationship exists between output and input voltages:V _(out) =R/R ₁ D _(τ) V _(in) where τ=RC.

The output of the low-pass filter 80 is multiplied by the coefficient μand thereafter provided as one of two input signals to another summingcircuit 82. On another input (line 84) that summing circuit 82 receivesthe sum (via summing circuit 86) of all of the phase error signalsεφ_(i) on line 63 (and associated lines from other local controllers)from all of the “n” PEMs as multiplied by the coefficient ν.

The signal ω′ is output from the summing circuit 82 and applied on line90 to all of the local controllers. As noted, this signal is comprised(see equation 2, above) of two components, one corresponding to thedifference between a selected retardation amplitude and the “average”retardation amplitude actually applied by the PEMs and another to thesum of the phase error signals of all PEMs. As will become clear, thissignal is used as a control parameter of the driving voltages of theindividual PEMs.

The output of the summing circuit 82 is also applied to an integrator 92that provides its output to a voltage controlled oscillator 96 (VCO)carried by the global controller 34. The VCO 96 places on line 100,which is common to all PEMs, a single driving frequency ω.

Returning to the local controller 32, the γ-multiplied signal ω′ summedat circuit 66 with the β-multiplied and inverted phase error signal εΦfor that particular PEM. The output (line 102) of that circuit isapplied to a D⁻¹ operator 104 followed by an integrator 106. Thesecomponents 104, 106 may be embodied as a low-pass filter 108 (see FIG.4) where the voltage signal out is described as follows:V _(out)=−1/R _(i) C∫D _(τ) ⁻¹ V _(in)(t)dt, and with τ=RC.

This voltage output is an amplitude control signal applied, viamultiplier 110, to modulate the constant amplitude output of the localcontroller VCO 40 so that the voltage amplitude applied to the PEM (vialine 46) is that for matching the overall or “average” resonantfrequency of all of the system PEMs. In short, the PEMs operate inunison (at the same resonant frequency), even though the individualretardation amplitudes are neither monitored nor directly controlled.

With all of the system PEMs operating in unison, the individualmechanical oscillation phases are locked to the phase of the commondriving frequency signal co. This ensures that all PEMs oscillate inphase so that the total retardation amplitude is certain to equal thesum of the individual PEM amplitudes. In this regard, the localcontrollers 32 employ another phase comparator 120. That comparatorcompares the phases of the PEM current (as provided by the signal fromthe current pickup 56) with that of the common drive signal ω andoutputs the difference (error) as the frequency input to the localcontroller's VCO 40, thereby locking the local PEM to the common, systemdrive frequency.

FIG. 5 depicts one preferred embodiment of a waveform generator(primarily represented by components 40 and 110 of the local controller32) for each PEM. The control voltage V from the integrator 106 is usedto control the output of two high-voltage power supplies 130 andassociated programmable regulators 132 of opposite polarity. The desiredwaveform is then obtained via a switch controller 134 that is driven bythe output of the VCO to switch the output between the two powersupplies. The resulting waveform has the same phase and frequency as theVCO output. The switch is implemented with high-speed, high-voltage,MOSFET transistors, which results in a simple circuit that does notintroduce significant additional phase errors.

This preferred implementation uses rectangular driving waveforms.Moreover, as long as the frequency of the rectangular waveform isrelatively close to the resonance frequency of the PEMs, the very narrowband pass characteristics of the latter (narrow resonance response)filter out the higher harmonics in the driving waveform. Consequently,there is no significant difference between driving the PEMs (nearresonance) with rectangular and sinusoidal signals. Of course, usingrectangular driving waveforms allows for simpler control of theamplitude and phase of the driving signal.

It will be appreciated that in the foregoing system the individual PEMdriving voltages generated by the global and local controllers in accordwith equations 1 and 2 force the individual PEM resonant frequencies toconverge to the common driving frequency. At the same time, the feedbacksystem generates a driving frequency that tracks an “average” of theindividual PEM resonant frequencies. The net result is that the commondriving frequency is always within the spread of resonant frequenciesand that this spread tends to collapse toward that common drivingfrequency. Thus, although the initial individual PEM resonantfrequencies may be different from each other, as well as from thedriving frequency, all resonant frequencies and the driving frequencysoon coalesce at a common value. From that point on, all PEMs in thestack operate in unison and are driven at resonance.

Further, both the driving voltage amplitudes and the common drivingfrequency also depend on the total amplitude error. This dependence issuch that the PEMs, while operating in unison, also track the selectedtotal retardation amplitude. The net result is a PEM stack that operateslike a single PEM, but at a much higher retardation amplitude.

If the manufacturing differences between PEMs are so large that a commondriving frequency that is an “average” of individual resonantfrequencies cannot drive all PEMs efficiently at startup, the commondriving frequency generated by the control system can be modified so asto drive most efficiently the PEMs farthest in resonant frequency fromthe average. This can result in an initial decrease in the spread ofresonant frequencies as the system warms up, to the point where themethod described above can be successfully applied. Alternatively, it isalso possible to drive each PEM at its particular resonant frequency atstartup, thus achieving an initial reduction in resonant frequencyspread that is sufficient for the preferred control method.

Moreover, if the manufacturing differences between PEMs are large,common resonance driving may result in some PEMs running at considerablyhigher temperatures than the others. Since the hotter PEMs are the onesbeing driven harder, they also contribute the most to the totalretardation amplitude. In such a situation, driving levels andretardation amplitudes can be balanced by controlling the ambienttemperature of the individual PEMs. The temperatures of the hotter PEMscan be maintained at elevated levels by external heating, thus reducingdriving amplitudes relative to those of the cooler PEMs. Ambienttemperature control can be used for coarse and slow resonant frequencytuning, while the finer and faster adjustments are still made bycontrolling the driving voltage amplitude.

FIG. 6 illustrates a controller that may be used with a single PEM 220so that the PEM is controlled in a manner to account for subtle changesin the PEM's resonant frequency, which changes may occur as the currentamplitude is increased to increase the retardation amplitude provided bythe PEM. The single-PEM controller 232 keeps constant both theretardation amplitude of the PEM and the actual operating frequency ofthe PEM, which frequency need not necessarily be the resonant frequency.

It is noteworthy that the controller 232 may be a modified version of alocal controller 32 as described above, but switchable, as by control ofthe computer 36, into the independent or single-PEM control mode whendesired by the user. As will be explained, in this mode, the computer 36may also be employed to supply certain reference signals to thecontroller 232.

In view of the dual-mode embodiment just noted, it can be appreciatedthat many of the controller components (enclosed by dashed lines 222)can be the same as those used in the local controller embodiment 32 and,as such, carry the same reference numbers in FIG. 6. A detaileddescription of these components, therefore, is not repeated here.

As noted, the key to simultaneous control of the PEM amplitude andoperating frequency is the separate control of the phase and theamplitude of the voltage waveform used to drive the PEM. In oneembodiment, the individual PEM 220 is driven by the square waveformgenerated as described above in connection with FIG. 5. The drivevoltage signal on line 52 and the current pickup on line 54 are used asinputs to amplitude and phase feedback loops.

As to phase regulation, a phase-lock loop circuit includes the phasecomparator 50, which receives as input the voltage signal on line 52,and the current pickup on line 54. The error signal εφ is summed with anexternal phase reference signal φ_(REF). The output of that summingcircuit 266 is applied as the frequency control input of the VCO afterpassing through a low-pass filter 268. As a result, the driving voltageand current waveforms are phase locked, but with a phase differencedetermined by the external phase reference signal φ_(REF) . . .

It will be appreciated that the external phase reference signal φ_(REF)can be selected at a level that would account for driving frequencydrift that occurs if the PEM's retardation amplitude is increased by anamount sufficient to change its resonant frequency. As noted, this driftis attributable, for example, to the power dissipation into the PEM(with attendant temperature change) when the PEM amplitude is increased.

For a given type of PEM (such as fused silica, calcium fluoride, zincselenide, etc.) the functional relationship between the drive amplitudeand resonant frequency changes may be employed, for example as a look-uptable processed by the computer 36 or in a control loop (describedbelow) to automatically establish the value of Φ_(REF) based upon thePEM's drive amplitude, thereby ensuring that a given operating frequencyis maintained-even though the PEM may not be driven at its resonantfrequency.

As to current regulation of the individual PEM 220, this is achieved bydirecting the PEM current signal from the rms 70, after inverting at270, to an input of a differential amplifier 272. The other input to theamplifier is from a user-selected reference current I_(REF). The outputof the amplifier is applied as the amplitude control of the waveformapplied to the PEM.

As to frequency regulation of the individual PEM 220, reference is madeto FIG. 7, which defines an outer feedback loop that provides the valueof Φ_(REF) (FIG. 6) for the frequency control of the VCO. FIG. 7diagrams an analog system that phase-locks the PEM driving voltage orcurrent to a frequency reference signal ω_(REF). The PEM driving voltageor current are input to a comparator 350 that provides its output, via alow-pass filter, as the control voltage that is applied as the Φ_(REF)input in the other, inner phase-lock circuit (FIG. 6). As shown in FIG.7, a “phase control” input can be used to adjust the phase between thePEM current or voltage and the frequency reference signal ω_(REF).

In lieu of the analog circuit shown in FIG. 7, one could employ adigital outer feedback loop that has a frequency counter for receivingan A/DC-converted PEM driving voltage or current. The output of thefrequency counter is compared to a set frequency by a digital processor,which correspondingly adjusts the value of Φ_(REF). Since the responsetime of this circuit can be relatively long, a relatively slow processorcan be used. Also, the stability, accuracy, and resolution of thefrequency counter only depend on how accurately and finely one wants toadjust the PEM's operating frequency.

While the present invention has been described in terms of preferredembodiments, it will be appreciated by one of ordinary skill in the artthat modifications may be made without departing from the teachings andspirit of the foregoing. As such, the scope of the invention is definedin the following claims and their equivalents.

1. A method of controlling a series of photoelastic modulators whereineach one of the series of “n” photoelastic modulators has a resonantfrequency and is operable in response to a drive voltage and to a drivefrequency, the method comprising the step of tuning the photoelasticmodulators during operation of the photoelastic modulators so that theresonant frequencies of all of the photoelastic modulators convergetoward a common resonant frequency.
 2. The method of claim 1 wherein thetuning step comprises: separately controlling the drive voltage of eachphotoelastic modulator; and providing to each of the photoelasticmodulators a common drive frequency.
 3. The method of claim 1 whereineach one of the series of photoelastic modulators is controllable toimpart a retardation value in electromagnetic radiation that is directedthrough the photoelastic modulator, the method further comprising thesteps of: selecting a reference retardation value; separatelycontrolling the drive voltage of each photoelastic modulator; providingto each of the photoelastic modulators a common drive frequency; andlocking the phase of oscillation of the photoelastic modulators to thecommon drive frequency so that the sum of the retardation values of allof the modulators matches the reference retardation value.
 4. The methodof claim 3 wherein the step of providing the common drive frequency isaccomplished in part by generating an error signal that includes the sumof the amplitudes of current applied to drive the “n” photoelasticmodulators.
 5. The method of claim 2 wherein the step of separatelycontrolling the drive voltage of each photoelastic modulator includesthe step of adjusting the amplitude of the drive waveform in response toa reference signal that substantially reflects an average resonantfrequency of the “n” photoelastic modulators.
 6. A system forcontrolling a series of “n” photoelastic modulators wherein each one ofthe “n” photoelastic modulators has a resonant frequency and is operablein response to a drive voltage and to a drive frequency, comprising: “n”local controllers, each one of the local controllers being connectedwith an associated one of the “n” photoelastic modulators; each localcontroller including: a drive waveform generator responsive to afrequency input signal and to an amplitude input signal for generating adrive signal waveform for driving the photoelastic modulator at a drivevoltage and a drive frequency; a phase comparator connected to the drivewaveform generator and to the photoelastic modulator for producing aphase error signal based upon the phase difference between the currentthrough the photoelastic modulator and the drive voltage signal appliedto the photoelastic modulator; and a current pickup circuit connected tothe drive waveform generator and for producing a current amplitudesignal indicative of the amplitude of the current waveform applied tothe photoelastic modulator; a global controller connected to each of thelocal controllers in a manner to receive the sum of the phase errorsignals produced by the phase comparators and the sum of the currentamplitude signals produced by the current pickups, wherein the globalcontroller includes: control circuit means for producing a drivefrequency signal for controlling the frequency input signal for all ofthe “n” drive waveform generators and for producing an amplitude signalfor controlling the amplitude input signal for all of the “n” drivewaveform generators.
 7. A method for controlling a resonant photoelasticmodulator, comprising the steps of: controlling the amplitude of thephotoelastic modulator oscillation; and controlling the frequency of thephotoelastic modulator oscillation by comparing the phase differencebetween a reference frequency generated external to the photoelasticmodulator and a current waveform that is applied for flowing currentthrough the photoelastic modulator to discern an error signal, andapplying the error signal for enabling oscillation of the photoelasticmodulator in phase with the reference frequency.
 8. The method of claim7 wherein the step of controlling the frequency of the photoelasticmodulator oscillation includes controlling the phase difference betweenthe voltage waveform of a drive signal applied to the photoelasticmodulator and the current flowing through the photoelastic modulator. 9.The method of claim 8 wherein the step of controlling the phasedifference includes the step of: phase locking the drive signal voltagewaveform to the waveform of the current flowing through the photoelasticmodulator.
 10. The method of claim 9 wherein the photoelastic modulatorhas a natural resonant frequency and wherein the phase locking stepincludes the steps of: comparing the phase difference of the drivesignal voltage waveform and the current waveform to discern an errorsignal based on the difference; adjusting the error signal; and applyingthe adjusted error signal for generating the drive signal, thereby toenable the photoelastic modulator to be oscillate at a frequency otherthan the natural resonant frequency.
 11. The method of claim 7 includingthe step of controlling the frequency of the photoelastic modulatoroscillation separately and independently of the amplitude of thephotoelastic modulator oscillation.
 12. The method of claim 7 includingthe step of controlling the amplitude of the photoelastic modulatoroscillation with a feedback signal.
 13. A controller for a resonantphotoelastic modulator, comprising: a drive waveform generatorresponsive to a frequency input signal and to an amplitude input signalfor generating a drive signal waveform for driving the photoelasticmodulator at a drive current amplitude and at a drive frequency; a phasecomparator connected to the drive waveform generator and to thephotoelastic modulator for producing a phase error signal based upon thephase difference between the drive signal waveform and a currentwaveform applied to the photoelastic modulator; and a phase-lock loopcircuit for receiving the phase error signal and for generating afrequency input signal based on that error signal, and for applying thefrequency input signal to the waveform generator.
 14. The controller ofclaim 13 wherein the photoelastic modulator has a resonant frequencythat is variable with the amplitude of the drive signal that is appliedto it, the system further comprising: a reference current amplitudecircuit for applying to the drive waveform generator an amplitude inputsignal having a value representing a selected current amplitude, and forchanging the value of the amplitude input signal in response to changesin the selected current amplitude; and tuning means for adjusting thephase error signal received by the phase-lock loop circuit in responseto changes in the value of the amplitude input signal, thereby toaccount for variations in the resonant frequency of the photoelasticmodulator.